7 problems

Low et al.'s optimal query-complexity conjecture for non-unitary dynamics
arXiv@arxiv
Low et al.'s conjecture. The optimal query complexity for block encoding $e^{-At}$ should scale as
Conjectureopennon-unitary-dynamics quantum-simulation query-complexity
1
Efficient Lie-algebraic simulation from polynomial dynamical Lie algebra dimension
arXiv@arxiv
Working conjecture. There exists a basis or representation of $\mathfrak{g}$ in which the preprocessing steps required by $\mathfrak{g}{\text - }{\rm sim}$ —basis construction and s…
Conjectureopendynamical-lie-algebras lie-algebras quantum-simulation
1
The conjecture on sampling decorated mixture indices for parallelized open-system simulation
arXiv@arxiv
Conjecture on decorated-mixture-index sampling. In future work, sampling of the decorated mixture index will be useful in parallelized algorithms which themselves might provide cru…
Conjectureopenopen-quantum-systems quantum-simulation tensor-networks
0
Conjecture on generic anomalous Trotter scaling in quantum chemistry
arXiv@arxiv
Consider quantum-chemistry Hamiltonians containing Coulomb potentials, and input states for which the Trotter error exhibits slower-than-standard scaling. Generic Coulomb-scaling c…
Conjectureopenquantum-chemistry quantum-simulation trotterization
0
Optimal recursive relation conjecture for product formulas
arXiv@arxiv
Optimal recursive relation conjecture. There is no $(2-\epsilon)$ -copy recursive formula.
Conjectureopenfree-lie-algebras product-formulas quantum-simulation
0
Universality of scaling in quantum advantage for extended physical systems
arXiv@arxiv
Universality conjecture. Given the simplicity of the Ising system, this scaling behavior may be a universal feature of quantum advantage in the simulation of extended physical syst…
Conjectureopenquantum-information quantum-simulation statistical-mechanics
2
Childs's higher-order splitting conjecture for Hamiltonian simulation
arXiv@arxiv
Consider simulation of a sparse Hamiltonian using splitting formulae, with spectral norm $Vert HVert$ and evolution time $Delta t$ . Higher-order splitting formulae reduce the compl…
Conjecturesolvedquantum-algorithms quantum-simulation
0

7 problems

Low et al.'s optimal query-complexity conjecture for non-unitary dynamics

Efficient Lie-algebraic simulation from polynomial dynamical Lie algebra dimension

The conjecture on sampling decorated mixture indices for parallelized open-system simulation

Conjecture on generic anomalous Trotter scaling in quantum chemistry

Optimal recursive relation conjecture for product formulas

Universality of scaling in quantum advantage for extended physical systems

Childs's higher-order splitting conjecture for Hamiltonian simulation